Entropic and enthalpic factors determining the thermodynamics and kinetics of carbon segregation from transition metal nanoparticles

Abstract

The free energy surface (FES) for carbon segregation from nickel nanoparticles is obtained from advanced molecular dynamics simulations. A suitable reaction coordinate is developed that can distinguish dissolved carbon atoms from segregated dimers, chains and junctions on the nanoparticle surface. Because of the typically long segregation time scale (up to μs), metadynamics simulations along the developed reaction coordinate are used to construct FES over a wide range of temperatures and carbon concentrations. The FES revealed the relative stability of different stages in the segregation process, and free energy barriers and rates of the individual steps could then be calculated and decomposed into enthalpic and entropic contributions. As the carbon concentration in the nickel nanoparticle increases, segregated carbon becomes more stable in terms of both enthalpy and entropy. The activation free energy of the reaction also decreases with the increase of carbon concentration, which can be mainly attributed to entropic effects. These insights and the methodology developed to obtain them improve our understanding of carbon segregation process across materials science in general, and the nucleation and growth of carbon nanotube in particular.